Simple layer potential and the first boundary value problem for a parabolic system on the plane

摘要

By the method of boundary integral equations, we construct a classical solution of the first initial-boundary value problem for a one-dimensional (with respect to x) parabolic system in a domain with nonsmooth lateral boundary for the case in which the right-hand sides of the boundary conditions only have continuous derivatives of order 1/2. We study the smoothness of the solution.